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FRM Part I · FRM Exam Part I · Hypothesis Testing

A 95% confidence interval for a regression-estimated mean return is computed as 2.1% to 5.9%. Which statement is the correct interpretation under the frequentist approach used in the FRM curriculum?

About 95% of intervals constructed this way from repeated samples would contain the true mean. The parameter is fixed and the interval varies by sample, so the 95% is not a probability statement about this specific interval or about individual observations.

  1. AThere is a 95% probability that the true mean lies between 2.1% and 5.9% for this particular sample
  2. BApproximately 95% of such intervals built from repeated samples would contain the true meanCorrect
  3. C95% of individual observations lie between 2.1% and 5.9%
  4. DThe sample mean has a 95% chance of lying between 2.1% and 5.9%

Explanation

The true mean is a fixed number; the interval is random across samples. The 95% refers to the long-run proportion of intervals that capture the true mean. Option 1 treats the parameter as random, and the interval is not about individual observations or about the sample mean, which is the interval's center (4.0%).

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